Calculate the steady-state photocurrent density in a reverse-biased, long pn diode. Consider a silicon pn diode at T = 300 K with the following parameters: Na = 10^16 cm^-3 Nd = 10^16 cm^-3 Dn = 25 cm^2 /s Dp = 10 cm^2 /s τn0 = 5 × 10^-7 s τp0 = 10^-7 s Assume that a reverse-biased voltage of VR =

Question

Calculate the steady-state photocurrent density in a reverse-biased, long pn diode. Consider a silicon pn diode at [latex]T=300 \mathrm{~K}[/latex] with the following parameters:

[latex]\begin{array}{ll}N_{a}=10^{16} \mathrm{~cm}^{-3} & N_{d}=10^{16} \mathrm{~cm}^{-3} \D_{n}=25 \mathrm{~cm}^{2} / \mathrm{s} & D_{p}=10 \mathrm{~cm}^{2} / \mathrm{s} \ au_{n 0}=5 imes 10^{-7} \mathrm{~s} & au_{p 0}=10^{-7} \mathrm{~s}\end{array}[/latex]

Assume that a reverse-biased voltage of [latex]V_{R}=5[/latex] volts is applied and let [latex]G_{L}=10^{21} \mathrm{~cm}^{-3}-\mathrm{s}^{-1}[/latex].

Accepted Answer

We may calculate various parameters as follows:

[latex]\begin{aligned}L_{n} &=\sqrt{D_{n} au_{n 0}}=\sqrt{(25)\left(5 imes 10^{-7} ight)}=35.4 \mu \mathrm{m} \L_{p} &=\sqrt{D_{p} au_{p 0}}=\sqrt{(10)\left(10^{-7} ight)}=10.0 \mu \mathrm{m} \V_{b i} &=V_{t} \ln \left(\frac{N_{a} N_{d}}{n_{i}^{2}} ight)=(0.0259) \ln \left[\frac{\left(10^{16} ight)\left(10^{16} ight)}{\left(1.5 imes 10^{10} ight)^{2}} ight]=0.695 \mathrm{~V} \W &=\left\{\frac{2 \epsilon_{s}}{e}\left(\frac{N_{a}+N_{d}}{N_{a} N_{d}} ight)\left(V_{b i}+V_{R} ight) ight\}^{1 / 2} \&=\left\{\frac{2(11.7)\left(8.85 imes 10^{-14} ight)}{1.6 imes 10^{-19}} \cdot \frac{\left(2 imes 10^{16} ight)}{\left(10^{16} ight)\left(10^{16} ight)} \cdot(0.695+5) ight\}^{1 / 2}=1.21 \mu \mathrm{m}\end{aligned}[/latex]

Finally, the steady-state photocurrent density is

[latex]\begin{aligned}J_{L} &=e\left(W+L_{n}+L_{p} ight) G_{L} \&=\left(1.6 imes 10^{-19} ight)(1.21+35.4+10.0) imes 10^{-4}\left(10^{21} ight)=0.75 \mathrm{~A} / \mathrm{cm}^{2}\end{aligned}[/latex]

Comment

Again, keep in mind that this photocurrent is in the reverse-biased direction through the diode and is many orders of magnitude larger than the reverse-biased saturation current density in the pn junction diode.

Question 14.5: Calculate the steady-state photocurrent density in a reverse...

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